Question

What is a normal curve and what are some of its uses?

What is a normal curve and what are some of its uses?

Homework Answers

Answer #1
  • A normal curve is a bell-shaped curve which shows the probability distribution of a continuous random variable.The term “bell curve” is usually used in the social sciences; in statistics, it’s called a normal distribution.
  • The mean (average) is always in the center of a bell curve or normal curve.
  • A bell curve / normal curve has only one mode, or peak. Mode here means “peak”; a curve with one peak is unimodal; two peaks is bimodal, and so on.
  • A bell curve / normal curve has predictable standard deviations that follow the 68/ 95 /99.7 rule.A standard deviation is a unit of measurement that can help you with figuring out where data items are likely to fall. For example, 68% of all measurements fall within one standard deviation either side of the mean. In other words, the bulk of your data will fall between -1 and +1 standard deviations from the mean. If you go out to two standard deviations, that percentage rises to 95; almost all (99.7%) of your data will fall within three standard deviations.
  • A bell curve / normal curve is symmetric. Exactly half of data points are to the left of the mean and exactly half are to the right of the mean.
  • The normal is also statistically convenient. It is represented by two parameters which are arguably the most basic statistics there are: the average and the variance (or standard deviation). The average is the most basic statistic there is.
  • It is used to determine the percentage of cases in a normal distribution within given limits.The Normal Probability Curve helps us to determine:
  • i. What percent of cases fall between two scores of a distribution.
  • ii. What percent of scores lie above a particular score of a distribution.
  • iii. What percent of scores lie below a particular score of a distribution.
  • It is used to compare two distributions in terms of- overlapping:-If scores of two groups on a particular variable are normally distributed. What we know about the group is the mean and standard deviation of both the groups. And we want to know how much the first group over-laps the second group or vice-versa at that time we can determine this by using the table area under NPC.
  • NPC helps us in dividing a group into sub-groups according to certain ability and assigning the grades:-When we want to divide a large group in to certain sub-groups according to some specified ability at that time we use the standard deviation units of a NPC as units of scale.
  • NPC is useful to normalize a frequency distribution:-In order to normalize a frequency distribution we use Normal Probability Curve. For the process of standardizing a psychological test this process is very much necessary.
  • To test the significance of observations of experiments we use NPC:-In an experiment we test the relationship among variables whether these are due to chance fluctuations or errors of sampling procedure or it is real relationship. This is done with the help of table area under NPC.
  • NPC is used to generalize about population from the sample:-We compute standard error of mean, standard error of standard deviation and other statistics to generalize about the population from which the sample are drawn. For this computation we use the table area under NPC.
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